Meanquad: Difference between revisions
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'''Meanquad''' is a [[4/1|double octave]]-repeating [[rank-2 temperament]] that tempers [[81/80]] in the 4.5.6 subgroup. Similarly to [[meantone]], it has a flat [[3/2]] as generator and equates [[5/4]] and [[81/64]]. It possesses [[MOS scales]] of the forms [[3L 4s (4/1-equivalent)|3L 4s<4/1>]], [[7L 3s (4/1-equivalent)|7L 3s<4/1>]], and [[7L 10s (4/1-equivalent)|7L 10s<4/1>]], which could be viewed as equivalents to the pentatonic, diatonic, and meantone chromatic scales respectively. | '''Meanquad''' is a [[4/1|double octave]]-repeating [[rank-2 temperament]] that tempers [[81/80]] in the 4.5.6 subgroup. Similarly to [[meantone]], it has a flat [[3/2]] as generator and equates [[5/4]] and [[81/64]]. It possesses [[MOS scales]] of the forms [[3L 4s (4/1-equivalent)|3L 4s<4/1>]], [[7L 3s (4/1-equivalent)|7L 3s<4/1>]], and [[7L 10s (4/1-equivalent)|7L 10s<4/1>]], which could be viewed as equivalents to the pentatonic, diatonic, and meantone chromatic scales respectively. For more techincal data, see [[7L 3s (4/1-equivalent)#Meanquad]]. | ||
== Interval chain (POTE tuning) == | == Interval chain (POTE tuning) == | ||
{|class="wikitable" | {|class="wikitable" | ||
Revision as of 03:15, 7 May 2023
Meanquad is a double octave-repeating rank-2 temperament that tempers 81/80 in the 4.5.6 subgroup. Similarly to meantone, it has a flat 3/2 as generator and equates 5/4 and 81/64. It possesses MOS scales of the forms 3L 4s<4/1>, 7L 3s<4/1>, and 7L 10s<4/1>, which could be viewed as equivalents to the pentatonic, diatonic, and meantone chromatic scales respectively. For more techincal data, see 7L 3s (4/1-equivalent)#Meanquad.
Interval chain (POTE tuning)
| Generators up | Cents |
|---|---|
| 0 | 0.0 |
| 1 | 696.8 |
| 2 | 1393.6 |
| 3 | 2090.4 |
| 4 | 387.2 |
| 5 | 1084.0 |
| 6 | 1780.8 |
| 7 | 77.6 |
| 8 | 774.4 |
| 9 | 1471.2 |
| 10 | 2168.0 |
| 11 | 464.8 |
| 12 | 1161.6 |
Tunings
17ed4 is the smallest tuning that can be said to support this temperament at all. Like 12edo, it can be viewed as the boundary between meanquad and the double-octave version of archy. Larger options include 24ed4 (12edo duplicate), 31ed4 and 55ed4.